a multilayer upper-boundary condition for longwave
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A Multilayer Upper-Boundary Condition for Longwave Radiative Flux toCorrect Temperature Biases in a Mesoscale Model
STEVEN M. CAVALLO, JIMY DUDHIA, AND CHRIS SNYDER
National Center for Atmospheric Research,* Boulder, Colorado
(Manuscript received 25 May 2010, in final form 9 September 2010)
ABSTRACT
An upper-level cold bias in potential temperature tendencies of 10 K day21, strongest at the top of the
model, is observed in Weather Research and Forecasting (WRF) model forecasts. The bias originates from
the Rapid Radiative Transfer Model longwave radiation physics scheme and can be reduced substantially by
1) modifying the treatment within the scheme by adding a multilayer buffer between the model top and top of
the atmosphere and 2) constraining stratospheric water vapor to remain within the estimated climatology in
the stratosphere. These changes reduce the longwave heating rate bias at the model top to 60.5 K day21.
Corresponding bias reductions are also seen, particularly near the tropopause.
1. Introduction
Use of mesoscale models has been shown to improve
forecasts while providing more detailed structure of the
atmosphere, particularly with regard to wind and pre-
cipitation over complex terrain (e.g., Mass et al. 2002),
hurricane intensity (e.g., Davis et al. 2008), and the lo-
cation and intensity of convective systems (e.g., Weisman
et al. 2008). Nevertheless, significant model biases re-
main. A recent application using the Weather Research
and Forecasting (WRF; Skamarock et al. 2008) model
and the Advanced Hurricane Research WRF (AHW;
Davis et al. 2008) model in experiments for the 2009
Atlantic hurricane season (hereafter AHW 2009) re-
vealed a bias in temperature, evident by a substantial
cooling trend, strongest near the model top. Here, we
examine the bias seen in the WRF model by recreating
AHW forecasts using the same domain (Fig. 1a) and
model configuration, and initialized using Global Fore-
casting System (GFS) analyses.
A temperature cooling bias is evident when viewing
a composite of 6-h forecasts from 0000 UTC 16 August
through 0000 UTC 22 August 2009. Figure 1b shows
the domain-averaged composite tendencies of potential
temperature u and radiative u heating rates. The local
time tendency of potential temperature ›u/›t decreases
from ;0 K day21 near the tropopause (;100 hPa) to
210 K day21 at the top model level. Longwave heating_uLW follows a similar pattern, but has larger magnitude
in the stratosphere. At these levels, ›u/›t is nearly equal
to the net radiative heating rate, indicating that _uLW is
partially offset by shortwave heating. To verify whether_u
LWexhibits a bias, standard tropical (TROP) and mid-
latitude summer (MLS) clear-sky longwave radiative
heating profiles (Ellingson et al. 1991; Clough and Iacono
1995) are shown for comparison. WRF _uLW diverges most
strongly from the standard profiles for p , 100 hPa,
with a value of 215 K day21 at 20 hPa compared to
25 K day21 in the standard profiles. Therefore, the cool-
ing trend in ›u/›t is a result of a bias in _uLW
, as high as
210 K day21 and increasing toward the model top.
Although the bias is most evident near the model top,
the rather large magnitudes of 210 K day21 seen here
could limit the stability of the model. Impacts of such a
cooling trend are especially likely to be seen in applica-
tions run over long periods of time, such as regional cli-
mate downscaling or data assimilation applications. For
example, data assimilation cycling applications use short-
term forecasts as a component in estimating the model
analysis. The forecasts used in AHW 2009 were initial-
ized using an ensemble Kalman filter (EnKF) consisting
of 96 members at 36-km grid spacing with 36 vertical
levels (Torn 2010), and analyses were cycled continuously
* The National Center for Atmospheric Research is sponsored
by the National Science Foundation.
Corresponding author address: Steven Cavallo, NCAR/Earth
System Laboratory, 3450 Mitchell Ln., Boulder, CO 80301.
E-mail: cavallo@ucar.edu
1952 M O N T H L Y W E A T H E R R E V I E W VOLUME 139
DOI: 10.1175/2010MWR3513.1
� 2011 American Meteorological Society
for 4 months. Most observations were assimilated in
lower-atmospheric levels, leaving little opportunity for
observations to correct deviations from the background
in upper levels. Owing to the long cycling period of the
analyses, this provides a good test case for examining the
longer-term impacts of the model bias.
A time–height section of the EnKF background u bias
for a 3-week period is shown in Fig. 1c. Biases are com-
puted with respect to GFS (EnKF-GFS) for the period
shown, and the data are filtered to exclude time scales
of 1 day or less. GFS, a global spectral model operated
by the National Centers for Environmental Prediction
(NCEP), is run with T382 (;35 km) horizontal reso-
lution, 64 vertical levels, and a model-top pressure of
0.2 hPa. Since the difference in vertical resolution is
substantial, and the model top is much higher in alti-
tude, we do not expect similar biases in GFS and AHW
2009. Note that u diverges most from GFS near the top
of the model (Fig. 1c). A slight warming trend is evident
with respect to GFS near the tropopause for 100 , p ,
250 hPa, and ;700 hPa. The warming trend ;100 hPa
is also evident in Fig. 1b, as most _uLW values are greater
than those expected from MLS, even though a consider-
able portion of the domain lies within the midlatitudes.
The bias produced by the existing boundary condition
of ;10 K day21 could potentially limit the stability of the
model, especially in very long runs (such as for regional
climate simulations) or when cycling a data assimilation
scheme for long periods. Here, we investigate the source
of the u bias and devise a method to correct it.
The biases discussed above are present when using
WRF with the Rapid Radiative Transfer Model (RRTM;
Mlawer et al. 1997). Model tops in mesoscale models
such as WRF do not generally extend to the top of the
atmosphere (TOA), and therefore assumptions must be
made to estimate the top of the model radiative boundary
conditions. In practice, model tops in mesoscale models
range from 10 to 100 hPa. In the WRF version of RRTM
(hereafter WRF-RRTM), the upper boundary is treated
similarly to general circulation models (GCMs); one
level is added between the model top and TOA. In the
extra layer, temperature is assumed to be isothermal,
and all mixing ratios are assumed to remain constant with
height, except O3, which is reduced by a factor of 0.6
(Iacono et al. 2000). However, model tops in GCMs
tend to be closer to the TOA, for example in the NCAR
Community Atmospheric Model (CAM), where it is
2.9 hPa (Collins et al. 2006). Standard clear-sky atmo-
spheric profiles show that temperature is nearly iso-
thermal in the lower stratosphere; however, above
;50 hPa it increases with height to the stratopause, lo-
cated near 1 hPa, by an average of ;40 K (Fig. 2a). In
addition to temperature, _uLW is expected to be most
FIG. 1. (a) Numerical test domain and (b) composite potential
temperature local time tendency, ›u/›t (green, dashed); longwave
radiative potential temperature heating rate, _uLW
(black); and net
radiative potential temperature heating rate (green) compared
with standard tropical (magenta) and midlatitude summer (ma-
genta, dashed) longwave radiative potential temperature heating
rate profiles from 6-h forecasts initialized with GFS at 0000 UTC
16 Aug–0000 UTC 22 Aug 2009. Profiles are averaged over the
entire test domain. Time–height section from the same domain, but
from a data assimilation cycling period from 0000 UTC 10 Aug to
0600 UTC 30 Aug 2009 using an EnKF with (c) potential tem-
perature bias (K) with respect to GFS (EnKF-GFS). In (b), the
gray shading represents the 61 standard deviation limits of _uLW
over the domain.
JUNE 2011 C A V A L L O E T A L . 1953
sensitive to carbon dioxide (CO2) and H2O, while O3,
although reaching a maximum ;5 hPa (Fig. 2b), is a rel-
atively weak absorber in the longwave bands (e.g.,
Manabe and Strickler 1964). Since CO2 is well mixed, and
since it is evident from Fig. 2c that H2O is well mixed in the
stratosphere, we hypothesize that assuming a more re-
alistic thermal structure between the model top and TOA
can improve the accuracy of radiative flux calculations.
We explore the above hypothesis through single-column
experiments using RRTM in section 2. Results from the
single-column experiments will then be applied to WRF
during the test period described above and discussed in
section 3. A summary of the results and changes to thw
WRF–RRTM scheme will be given in section 4.
2. Single-column experiments
a. Experimental setup
We use a stand-alone version of RRTM version 3.1
(available online at http://rtweb.aer.com), with standard
midlatitude winter (MLW), MLS, subarctic winter (SAW),
and TROP atmospheric profiles provided. The standard
profiles provided are from the Intercomparison of Ra-
diation Codes Used in Climate Models (ICRCCM;
Ellingson et al. 1991), which are based on reference at-
mospheric profiles by the Air Force Geophysics Labo-
ratory (AFGL; Anderson et al. 1986). Heating rates
based upon these standard profiles have been validated
for RRTM with line-by-line model calculations (Mlawer
et al. 1997) and observations (Clough and Iacono 1995).
Control runs use the exact 36 vertical levels from AHW
2009, plus an additional level at the TOA that uses the
same assumptions as WRF-RRTM. In the experiment
runs, we replace the additional TOA level by a buffer
zone, with a variable number of levels, above the pressure
at the model top ( ptop). Experiments are performed using
pressure increments of Dp 5 28, 24, and 22 hPa in the
buffer zone, inclusive of 1 and 0 hPa. For example, ptop 5
20 hPa with a pressure increment of Dp 5 24 hPa in-
cludes buffer levels of 16, 12, 8, 4, 1, and 0 hPa. These
pressure intervals are chosen as a compromise to resolving
a realistic temperature profile while not significantly de-
grading the computational efficiency.
Experiments are designed to account for various at-
mospheric conditions based on the standard MLW, MLS,
SAW, and TROP atmospheres. In the buffer zone, the
temperature profile is extended above the model top using
the vertically varying mean lapse rate from the standard
MLW, MLS, SAW, and TROP profiles (recall Fig. 2a).
Below the buffer zone, these initial temperature profiles
are linearly interpolated to the given WRF vertical pres-
sure levels in the control case and the experiments. In
the control case, volume mixing ratios of CO2 and O3 are
converted from the average mass mixing ratios in the 2009
AHW experimental domain, while water vapor is con-
verted from mean relative humidity; all other gaseous
mixing ratios are set to zero as in WRF-RRTM. In the
experiments, all gaseous mixing ratios are interpolated
from their respective standard profiles. All cases assume
clear-sky conditions.
FIG. 2. The standard MLW (blue), MLS (red), SAW (cyan),
TROP (green), and mean (boldface black) vertical profiles of (a)
temperature (K), (b) ozone (ppmv), and (c) water vapor (ppmv).
See text in section 2 for more details regarding these profiles.
1954 M O N T H L Y W E A T H E R R E V I E W VOLUME 139
b. Single-column results
Figure 3 shows the differences between the control
and experimental _uLW
at the top model level from their
respective standard values. To explore a more complete
range of solutions, experiments were repeated using
ptop 5 0.2, 0.5, 1, 5, 10, 20, 50, 100, 200, and 300 hPa
employing the same WRF h levels in all experiments.
In the SAW control, the longwave cooling bias increases
with increasing (decreasing) model-top height (pressure),
with a bias of 22 K day21 for ptop 5 20 hPa to values
exceeding 220 K day21 with ptop 5 1 hPa (Fig. 3a). This
result is rather surprising, and indicates the closer ptop and
TOA, the stronger the bias as the vertical resolution is
degraded for ptop closer to the TOA. The buffer zone
reduces the bias to 61 K day21 for 1 , ptop , 200, with
the strongest reductions using Dp 5 24 hPa. Similar
patterns exist for the MLW, MLS, and TROP cases,
where single-column RRTM experiments show a sub-
stantial reduction in the _uLW bias (Figs. 3b–d).
The buffer itself may be problematic for model tops
near the stratopause (ptop , 5 hPa). Note that although
the bias remains large for such ptop, it is substantially
reduced with a buffer. In the configuration here, as ptop
decreases, there are fewer levels in a given layer near the
stratopause than with a buffer for greater ptop. To test
whether there is a sensitivity to the number of model
levels near the stratopause, we repeat the above for the
MLS experiment (recall Fig. 3c), where biases for ptop ,
5 hPa were largest. In the experiment here, we define
FIG. 3. Longwave radiative heating rates at the top model level minus the respective standard heating rate at the
equivalent pressure level ( _uLW,model � _uLW,standard) as a function of model-top pressure based upon standard (a) SAW,
(b) MLW, (c) MLS, and (d) TROP atmospheric vertical profiles. The difference in the control experiment is shown in
blue. Experiments using pressure intervals of 28, 24, and 22 hPa between the model top and TOA are shown with
the dashed, solid, and dashed–dotted red contours, respectively. Note the differences shown are not continuous
profiles.
JUNE 2011 C A V A L L O E T A L . 1955
WRF h levels to be of constant geopotential thickness
(1.4 km) for p , 20 hPa based on the thickness of the
AHW configuration near its model top of 20 hPa. This
new vertical-level distribution is compared to that of the
original experiment in Fig. 4a, and shows the relatively
sparse distribution of vertical levels around the strato-
pause previously. Biases are reduced considerably for
ptop , 5 hPa by having better vertical resolution near
the stratopause (Fig. 4b). From further experiments (not
shown), we can attribute the remaining disagreement to
differences in the vertical resolution of the troposphere
between the standard profile and experiments. The re-
sults here show that for ptop , 5 hPa, the remaining
biases can be reduced by having sufficient vertical res-
olution near the stratopause, which here is achieved by
defining a vertical grid spacing with a constant geo-
potential thickness of 1.4 km in the buffer.
In addition to temperature, longwave radiative fluxes
are also sensitive to concentrations of gaseous absorbers.
Currently, the effects of three gaseous absorbers are
computed in WRF-RRTM: H2O, CO2, and O3. Sensi-
tivity tests (not shown) indicated that cooling rates re-
spond largely to the change in CO2 for ptop , 200 hPa; for
ptop . 200 hPa, the largest response shifts to H2O. There
is a small response to changing O3, except when ptop is
near the stratopause. Thus, in addition to those for tem-
perature, careful assumptions in CO2 and H2O in the
buffer zone are important in obtaining accurate _uLW
from
RRTM. We next apply the buffer method to a fully three-
dimensional case using the AHW model.
3. Application to the WRF model
The new modifications to WRF-RRTM discussed in
section 2 are now applied to the same AHW forecasts
discussed in section 1. The model domain, configuration,
and physics schemes are as in Torn (2010), where longwave
radiation is computed with the RRTM (Mlawer et al. 1997)
and shortwave radiation with the National Aeronautics
and Space Administration (NASA) Goddard shortwave
radiation schemes (Chou and Suarez 1994). Note that
when applying the modifications to WRF-RRTM, the
additional vertical levels are only added to the RRTM
radiation scheme itself, and no information about the extra
levels is carried outside of it. For ptop 5 20 hPa, five ad-
ditional buffer levels are used within RRTM, and the total
increase in model run time is ;2.7%. Since the model run
time is largely dependent on the number of vertical levels,
and the number of vertical levels is determined by Dp (here
Dp 5 24 hPa), consideration should be given when
choosing Dp for model tops farther removed from the
TOA in order to avoid unnecessary increases in run time.
We composite a total of thirteen 6-h forecasts, initialized
every 12 h using GFS analyses beginning at 0000 UTC
16 August and ending at 0000 UTC 22 August 2009 with
boundary conditions derived from GFS forecasts every
3 h. The simulations are performed on a Lambert con-
formal projection, on a variably located finescale domain
within the coarse domain (Fig. 1a) centered on the storms
of interest for AHW 2009, using 424 3 325 x and y grid
points, respectively, and 12-km horizontal resolution.
FIG. 4. (a) Distribution of WRF h levels as a function of pressure for the experiment using a pressure interval of
24 hPa (red) and when defining WRF h levels using a constant thickness of ;1.4 km (denoted as 1 dz in the legend,
where 1 dz 5 1 3 1.4 km) between 20 hPa and the model top (green) for a model top of 0.2 hPa. (b) Longwave
radiative heating rates at the top model level minus the MLS standard heating rate at the equivalent pressure level
( _uLW,model � _uLW,standard) as a function of model-top pressure using the vertical levels shown in (a) based on the MLS
atmospheric vertical profile. Note the differences shown in (b) are not continuous profiles.
1956 M O N T H L Y W E A T H E R R E V I E W VOLUME 139
Soon after the experiments began, an erroneous fea-
ture was found with regard to water vapor. It was found
to arise in the handling of water vapor in the WRF
PreProcessing System (WPS) version 3.0.1 when water
vapor is not provided from the input data, such as the
case with GFS gridded binary (GRIB) data until January
2010, where water vapor extended only to 100 hPa. At
levels where p , 100 hPa, relative humidity was assumed
to decrease proportionally with pressure, with a value of
5% at 50 hPa. This resulted in volume mixing ratios in-
creasing with height to ;2 3 102 ppmv at ptop for ptop 5
20 hPa. Recall from Fig. 2c that volume mixing ratios
should exhibit little variance ;5 ppmv. We hereafter
separate our results into those where H2O is left un-
changed (‘‘without H2O adj.’’) and where H2O is fixed
to 5 ppmv at all levels where p , 100 hPa (‘‘full
modifications’’).
At ptop, TROP and MLS _uLW are 63.0% (9.9 K day21)
and 66.7% (10.5 K day21) lower than the control case,
respectively (Fig. 5a). Adding the buffer zone reduces the
cooling rates by 48.7%, or ;7 K day21 with respect to the
control at the top model level, with reductions to levels as
far as ;250 hPa (Fig. 5b). The water vapor adjustment
reduces cooling rates an additional 2.5 K day21 to cooling
rates within 60.5 K day21 of the standard cooling rates.
Stronger cooling, up to 0.5 K day21, is seen in the upper
troposphere (;200 hPa) when including the water vapor
adjustment. A decrease in the downward flux from less
stratospheric water vapor results in enhanced cooling
rates, and leads to an increase in upper-tropospheric
clouds in areas close to saturation. Thus, the net changes
eliminate the stratospheric cooling bias, and addition-
ally correcting the stratospheric water vapor reduces the
upper-tropospheric warming trend (recall Figs. 1b and 1c).
The spatial distribution of _uLW
at the top model level ex-
hibits a zonal cooling pattern in the control, with increased
cooling rates ranging from 8 to 13 K day21 from south to
north (Fig. 6a). This latitudinal _uLW pattern is associated
with warmer stratospheric temperatures present during
the summer over higher latitudes. The modifications in_uLW are reflected in ›u/›t, with u being 2–4 K warmer on
average at forecast hour 6 (Fig. 6b).
4. Summary
WRF (AHW) forecasts initialized with both GFS and
EnKF analyses exhibit a negative potential temperature
tendency bias of up to 10 K day21, greatest at the model
top. The bias was found to arise when using WRF with
the RRTM longwave radiation physics scheme. With the
expectation that gaseous longwave absorbers are well
mixed at levels where the bias is observed, it was hy-
pothesized that previous assumptions of an isothermal
layer between the model top and the top of the atmo-
sphere lead to the flux divergence errors at the upper
model boundary resulting in the bias.
Results reveal that the temperature bias can be re-
duced by 1) creating buffer levels between the model top
and the top of the atmosphere by extending a tempera-
ture profile above the model top based on the mean,
FIG. 5. Composite vertical longwave potential temperature (a) heating rates and (b) differences from the control
case ( _uLW,experiment
� _uLW,control
) of 6-h forecasts initialized with GFS from 0000 UTC 15 Aug to 0000 UTC 22 Aug
2009. The control case (no change in the RRTM longwave radiation scheme) is shown in black, while the TROP and
MLS atmospheric profiles are shown by the magenta and dashed magenta contours, respectively. The experiment
where only a buffer layer is added with Dp 5 24 hPa is shown in green, while the experiment with the buffer layer and
an adjustment to the stratospheric water vapor are shown in blue. All profiles are averaged over the entire test
domain (See Fig. 1a). In (a), the light (dark) gray shading represents the 61 standard deviation limits of _uLW for the
full modifications (Control) experiments over the domain.
JUNE 2011 C A V A L L O E T A L . 1957
vertically varying standard atmospheric lapse rate and
2) if necessary, setting water vapor mixing ratios for p ,
100 hPa to a constant 5 ppmv. The former yields larger
downward radiative fluxes at the upper model boundary
resulting in a smaller flux divergence, primarily affecting
model levels close to the model top. The latter results in
less cooling from reduced longwave absorption by water
vapor molecules for p , 100 hPa and, further, results in
greater upper-tropospheric cooling. The combined effects
reduce longwave radiative cooling rates for ptop . 5 hPa
to within 60.5 K day21 of the standard rates obtained
in the line-by-line clear-sky calculations of Clough and
Iacono (1995). Cooling rates are now in more consis-
tent agreement with those found using relatively high
vertical resolution and upper boundaries of ;0.1 hPa
(Mlawer et al. 1997). Similar treatment of the upper
boundary is made using the Rapid Radiative Transfer
Model for GCMs (RRTMG) longwave radiation scheme
in WRF, and can be corrected using this method. In
general, this method is applicable to numerical models
using longwave radiation schemes where the model top
differs substantially from the top of the atmosphere and
requires minimal computational expense.
These results emphasize the importance of carefully
specifying radiative fluxes at the upper boundaries of
mesoscale models, especially those with model tops sig-
nificantly below the top of the atmosphere. They further
emphasize the sensitivity of longwave heating to strato-
spheric trace gases, especially water vapor; great care
should be placed on the assumptions of these concen-
trations when data are either unavailable or unreliable.
Although the method here substantially reduces the
magnitudes of the longwave biases for all model top levels
tested, a considerable bias remains for model tops near the
stratopause, which can be further reduced by increasing
the vertical resolution of the model and buffer levels near
the stratopause.
Acknowledgments. Support for the second author was
by the Department of Energy through DOE-ARM
Grant DE-FG02-08ER64575.
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FIG. 6. Composite potential temperature (a) heating rate differences ( _uLW,experiment � _uLW,control) and (b) changes in
6-h forecasts of potential temperature (uexperiment,forecast 2 ucontrol,forecast) at the top model level between the control
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